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butalik [34]
1 year ago
7

10. When Raphael solved the system below by using the method of elimination, he changed the second equationto -8x – 2y = -2. Wha

t property justifies this manipulation?8x + 3y = 74x + y = 1
Mathematics
1 answer:
Alex17521 [72]1 year ago
5 0

\begin{gathered} 8x+3y=7\ldots eqn(1) \\ 4x+y=1\ldots.eqn(2) \end{gathered}

The property that justifies multiplying through eqn(2) by -2 is;

the rationalization to align the coefficients of x in both equations with a view to eliminating the terms in x.

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Complete each congruence statement by naming the corresponding angle or side (odd questions only)
IrinaK [193]

Answer:

Step-by-step explanation:

Corresponding parts of the congruent triangles are congruent [CPCTC]

By using this property of congruent triangles,

15). ΔABC ≅ ΔABR

     BC ≅ BR [By CPCTC]

16). ΔJIH ≅ ΔJIW

     ∠HJI ≅ ∠WJI [By CPCTC]

17). ΔBDC ≅ ΔBDJ

     ∠CBD ≅ ∠JBD [By CPCTC]

8 0
2 years ago
What are the exact values of sin theta cos theta tan theta if (3,-4) is a point on the terminal side of theta?
malfutka [58]
\bf (\stackrel{a}{3}~,~\stackrel{b}{-4})\impliedby \textit{now let's find the \underline{hypotenuse}}
\\\\\\
\textit{using the pythagorean theorem}
\\\\
c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}
\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}
\\\\\\
c=\sqrt{3^2+(-4)^2}\implies c=\sqrt{25}\implies \boxed{c=5}

\bf -------------------------------\\\\
sin(\theta )=\cfrac{\stackrel{opposite}{-4}}{\stackrel{hypotenuse}{5}}\qquad cos(\theta )=\cfrac{\stackrel{adjacent}{3}}{\stackrel{hypotenuse}{5}}\qquad tan(\theta )=\cfrac{\stackrel{opposite}{-4}}{\stackrel{adjacent}{3}}
6 0
3 years ago
What is the volume of a right circular cylinder with a base diameter of 17.5 ft and a height of 24.5 ft?
Natasha_Volkova [10]

Answer:

The volume of a right circular cylinder with a base diameter of 17.5 ft and a height of 24.5 ft is:

5889.95 ft³

Step-by-step explanation:

We are given a base diameter of a right circular cylinder as :

d = 17.5 ft.

hence radius of cylinder i.e. r =d/2 = 8.75 ft.

height of the cylinder = 24.5 ft.

now we know that volume of cylinder i.e. V is given by :

V = πr²h

putting the value of r and h in the given formula to obtain the volume

V = 3.14×(8.75)²×24.5

   = 5889.95 ft³

hence, the volume of a right circular cylinder with a base diameter of 17.5 ft and a height of 24.5 ft is:

5889.95 ft³

3 0
3 years ago
Read 2 more answers
Apply the distributive property to create an equivalent expression.<br> 6(a + 2b + 3c) =
Alina [70]
6a+ 12b+ 18c

Hope this is correct...plz let me know
3 0
3 years ago
Read 2 more answers
Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are sum
Naddika [18.5K]

Answer:

P(A) = 86/100

P(B) = 79/100

P(A') = 14/100

P(A U B) = 95/100

P(A' U B) = 84/100

Step-by-step explanation:

i. P(A) = number of disks with high shock resistance/total number of disks

= (70+16)/100

= 86/100

ii. P(B) = number of disks with high scratch resistance/total number of disks

= (70+9)/100

= 79/100

iii. P(A') = number of disks without high shock resistance/total number of disks

= (100-86)/100

= 14/100

iv. P(AUB) = number of disks with high shock resistance or high scratch resistance/total number of disks

= (70+9+16)/100

= 95/100

v. P(A'UB) = number of disks without high shock resistance or with high scratch resistance/total number of disks

= (5+9+70)/100

= 84/100

3 0
3 years ago
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